What does the Fourier transformed image mean?
Have a look at this explanation of the two dimensional Fourier Transform applied to an image.

The way I read it is that it somewhat mirrors the diagonal structure of the 'X', as that is where most of the 'image energy' is, so that are the lines you highlighted. Because the image is fairly uniform in colour, most of the components are low-frequency (ie close to the centre of the 2DFT image).

Disclaimer: I'm not really that familiar with a 2D version either, as I mainly have experience with using FFTs in speech processing.